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My 07 Z06 has had some popping/crackling noises that come and go from the front driver Bose speaker. It wasn't that bad as it wasn't always there but its getting worse and super annoying. Now the main issue id when entering my car and the car radio is turned on (either in Acc. mode or starting the car) the speaker goes crazy and super loud. Turning the volume up or down does nothing for the noise. Its a noise I cant explain but I would guess is some sort of interference. Its goes away after 5 seconds or so and then the normal popping/cracking of the speaker comes into play. Again, this part is hit or miss and is volume controlled. Anyone ever heard of this before or have any ideas what it is? I really don't want to throw random parts at it trying to fix it. I'd sell it before I spent $1000 trying. LOL
Kinda sounds like the radio itself may be the issue.
You can swap door speakers left to right to rule them out (free except for your time). That would be the easiest fix, and cheapest if it was just the 3.5" twiddler (you could even yank the center dash speaker to use it as a free replacement). However, the 'full volume' issue tells me it probably isn't a speaker.
Amp would be harder to troubleshoot unless you have someone local who can hook up a C2R-GM24 type adapter and feed the amp a known good signal. I have a hacked up one that I could mail to you as a loaner if needed. An iPod with headphone to RCA adapter cord is a good test source.
To test the radio you'd need to connect something like a modified Add-GM24 w/RCA's to an external amp to see what the radio is putting out. I have a harness I can mail, but you'd have to get an amp and speaker(s) locally. An old home entertainment system or anything that can amplify RCA inputs would work, it doesn't really have to be car audio gear for a test.